Gold Seal Lesson:
Planning Stairs

Copernicus Education Gateway

 

Subject:

Mathematics

Grade:

 

 

9-12

 

 

ICLE Standards:

 

 

Geometry and Measurement: Measure lengths

Algebra: Calculate and compare slopes

Trigonometry:   Find missing parts of right triangles

Problem Solving:   Develop acceptable compromises

Use research skills

 

 

Performance Task:

 

 

Measure the tread and rise on three sets of stairs. Calculate the overall rise and run of each of the stairs. Compare the slope of each step to the entire stairway. 

An acceptable stair ratio is 8" rise and 11" tread. Draw a scale drawing of steps needed to reach a 42" porch. A facing board is to be used on each side of the steps to support them. It will be cut like this.

 

 

 

Knowledge / Skills:

 

 

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. M.1

Understand the properties and classification triangles by sides (i.e., scalene, isosceles, and equilateral). M.16

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min). Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis. M.33

Perform the general solution of triangles by using the law of sines and law of cosines to obtain the angle and side length measurements of any triangle. M.54

Apply reading skills while reading textbooks in courses other than English. ELA.26

 

 

Rubric:

 

 

4 POINTS: Student explains the need for the rise/tread ratio to be constant and within building codes. Student can find the angle to set the saw. Student is able to measure components of the problem correctly.

 

 

3 POINTS: Student needs help figuring the angle of the saw. Student does not explain clearly the need and method for planning an acceptable stairway- Student does not complete one of the measuring tasks.

 

 

2 POINTS: Student cannot figure the angle of the saw even after receiving help- Student does not measure two of the required stairs. Student cannot explain why the slope of a stairway is important.

 

 

1 POINT: Student tries to do the problem by simply sketching stairways.

 

 

Keywords:

 

 

ALGEBRA
ANGLES
READING
INFORMATION GEOMETRY
TRIANGLES
MEASUREMENT
PROBLEM SOLVING
COMPUTATION 
RATIOS

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [x] - 10 [x] - 11 [x] - 12 [x]

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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